This is KILLING me... how can a massless object have a non-zero net force, yet NOT have infinite acceleration?

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G

gopunk

Lifer
Jul 7, 2001
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F=ma, if m=0, then the only way to get a net force would be to set acceleration equal to infinite, right? am i missing something?

the problem is this, there is a frictionless rod, and a massless ring that is on the rod. a string is tied to the ring. there is a wave propagating on the string, and we have to describe the motion of the ring. but how can the f*ing ring move? i thought it was infinite acceleration, but i have a feeling i'm wrong.
 
H

Heisenberg

Lifer
Dec 21, 2001
10,621
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Hmm...that's kind of a weird problem statement. I don't have a clear idea of what they're asking for. Can you give more detail?
 
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Frosty3799

Diamond Member
Nov 4, 2000
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<< Hmm...that's kind of a weird problem statement. I don't have a clear idea of what they're asking for. Can you give more detail? >>



and draw a pic, if you can?
 
db

db

Lifer
Dec 6, 1999
10,575
292
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Wouldn't the ring follow the natural path of the wave, in an up/down similar to an ociliscope wave wiggling over a vertical grid mark where those two points continuously intersect?
 
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Frosty3799

Diamond Member
Nov 4, 2000
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<< situation is like this >>




i think the ring is to just keep the string attached to the rod, but not effect the movement at all, and no, anything that is massless (quite improbable, but it could have a minimal mass) and connected to something else that is moving would just move right along with the moving object
 
G

gopunk

Lifer
Jul 7, 2001
29,239
2
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<<

<< situation is like this >>




i think the ring is to just keep the string attached to the rod, but not effect the movement at all, and no, anything that is massless (quite improbable, but it could have a minimal mass) and connected to something else that is moving would just move right along with the moving object >>




okay so basically if the book was being truthful, i'm right and it *would* have infinite acceleration, but since the book is taking a few liberties, it doesn't?
 
H

Heisenberg

Lifer
Dec 21, 2001
10,621
1
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Ok, that makes sense. I think the ring in this case is just a convenient way to visualize what's happening at the boundary.
 
db

db

Lifer
Dec 6, 1999
10,575
292
126
If you don't have to worry about friction, or about mass, then you get the resultant action, which would be....
 
H

HappyPuppy

Lifer
Apr 5, 2001
16,997
2
71
If you can find the solution to infinite acceleration, NASA has a job waiting for you. Starting pay $18,000,000/yr.
 
H

Heisenberg

Lifer
Dec 21, 2001
10,621
1
0


<< okay so basically if the book was being truthful, i'm right and it *would* have infinite acceleration, but since the book is taking a few liberties, it doesn't? >>



Not quite. The ring being massless has the effect of the making the RHS of the equation 0 and therefore making the acceleration not matter at all.
 
F

Frosty3799

Diamond Member
Nov 4, 2000
3,795
0
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<<

<< okay so basically if the book was being truthful, i'm right and it *would* have infinite acceleration, but since the book is taking a few liberties, it doesn't? >>



Not quite. The ring being massless has the effect of the making the RHS of the equation 0 and therefore making the acceleration not matter at all. >>



right, the accell of the ring isnt important to the problem
 
P

Polgara

Banned
Feb 1, 2002
127
0
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Addressing only one point of the original question (since this problem is beyond my ability).

F=ma

If m=0, then F=0 for ANY value a. Even infinity

since

0i=0 for all i

Which is why the tension force is exactly equal to the normal force acting on the string.


Sarah <== ***twirls hair with finger***
 
D

dirtboy

Diamond Member
Oct 9, 1999
6,745
1
81
Would not the ring move in accordance to the wave being applied by the string? In the diagram, the string is moving up and down, so I don't think the acceleration would be infinite. It may accelerate quite quickly, but over time it is going to be going in a direction 180 degrees opposite of the direction it is accelerating in.

This is a fascinating question. I'd be curious to know the actual answer.

Could not an obect have no mass, when in space? A frictionless rod may be impossible to manufacture, but this scenerio could occur in outer space?

Just my random thoughts.
 
G

gopunk

Lifer
Jul 7, 2001
29,239
2
0


<<

<< okay so basically if the book was being truthful, i'm right and it *would* have infinite acceleration, but since the book is taking a few liberties, it doesn't? >>



Not quite. The ring being massless has the effect of the making the RHS of the equation 0 and therefore making the acceleration not matter at all. >>



eh... well i now realize that i'm just supposed to ignore the details, but i don't see what you're saying. if F is non-zero, and m is zero, acceleration *must* be infinite, right? well, in math at least... i say F is non-zero because the ring moves. an object that is standing still can't just move by itself, right?

but of course you are right, this doesn't do anything for the problem itself in the spirit it was intended.
 
H

Heisenberg

Lifer
Dec 21, 2001
10,621
1
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You have to remember that the LHS of the equation is the sum of the forces acting on the ring. In the first case, it's the sum of the normal force and the tension. Since the sum equals zero, the normal force equals the tension.
 
G

gopunk

Lifer
Jul 7, 2001
29,239
2
0


<< You have to remember that the LHS of the equation is the sum of the forces acting on the ring. In the first case, it's the sum of the normal force and the tension. Since the sum equals zero, the normal force equals the tension. >>



only at equilibrium though, right? if the ring moves, shouldn't there be a net force? i mean, the horizontal components of normal and tension shoudl cancel, but you're still left with a vertical componet of tension, which is what makes the ring slide up and down.

i get the feeling i'm missing something... ;)
 
F

Frosty3799

Diamond Member
Nov 4, 2000
3,795
0
0


<<

<< You have to remember that the LHS of the equation is the sum of the forces acting on the ring. In the first case, it's the sum of the normal force and the tension. Since the sum equals zero, the normal force equals the tension. >>



only at equilibrium though, right? if the ring moves, shouldn't there be a net force?

i get the feeling i'm missing something... ;) >>



well it will always return to equilibrium, meaning the net force was still 0. if it is "forced" up the rod by the string, then it will also be "forced" back down
 
C

Capn

Platinum Member
Jun 27, 2000
2,716
0
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It's just a convention, you shouldn't dwell on it. Since the ring has no mass, it takes no force to move it. Acceleration can be any value, and need not be infinite. It's a simplification so you can actually set boundary conditions and mathmatically solve the problem without running any computer codes.
 
SagaLore

SagaLore

Elite Member
Dec 18, 2001
24,036
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<< This is one of those questions like can God create a boulder that is too heavy for even him to lift. >>




!

I guess that proves that science isn't real!

:)
 
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